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Understanding the decision-making processes of large language models is critical given their widespread applications. To achieve this, we aim to connect a formal mathematical framework - zigzag persistence from topological data analysis -…
Complex networks, which are the abstractions of many real-world systems, present a persistent challenge across disciplines for people to decipher their underlying information. Recently, hyperbolic geometry of latent spaces has gained…
Hyperbolic geometry has emerged as an effective latent space for representing complex networks, owing to its ability to capture hierarchical organization and heterogeneous connectivity patterns using low-dimensional embeddings. As a result,…
In this paper, we show that high-performing embedding models organize their embedding spaces in a consistent way. We evaluate 25 contemporary embedding models on five MTEB tasks spanning four diverse task categories (retrieval, bitext…
The study of phase transitions using data-driven approaches is challenging, especially when little prior knowledge of the system is available. Topological data analysis is an emerging framework for characterizing the shape of data and has…
Persistent homology is a popular method for computing topological features of (metric) data. Standard approaches based on the \v{C}ech or Rips filtration are stable under small perturbations of the data, but highly sensitive to outliers.…
Overconfidence is a common issue for deep neural networks, limiting their deployment in real-world applications. To better estimate confidence, existing methods mostly focus on fully-supervised scenarios and rely on training labels. In this…
Biological and physical systems often exhibit distinct structures at different spatial/temporal scales. Persistent homology is an algebraic tool that provides a mathematical framework for analyzing the multi-scale structures frequently…
With the emergence of deep learning, metric learning has gained significant popularity in numerous machine learning tasks dealing with complex and large-scale datasets, such as information retrieval, object recognition and recommendation…
In semi-supervised learning, methods that rely on confidence learning to generate pseudo-labels have been widely proposed. However, increasing research finds that when faced with noisy and biased data, the model's representation network is…
Biomolecular structure comparison not only reveals evolutionary relationships, but also sheds light on biological functional properties. However, traditional definitions of structure or sequence similarity always involve superposition or…
Persistence diagrams (PDs), often characterized as sets of death and birth of homology class, have been known for providing a topological representation of a graph structure, which is often useful in machine learning tasks. Prior works rely…
Nowadays, supervised learning is commonly used in many domains. Indeed, many works propose to learn new knowledge from examples that translate the expected behaviour of the considered system. A key issue of supervised learning concerns the…
The latent space model is one of the well-known methods for statistical inference of network data. While the model has been much studied for a single network, it has not attracted much attention to analyze collectively when multiple…
In traditional topology optimization, the computing time required to iteratively update the material distribution within a design domain strongly depends on the complexity or size of the problem, limiting its application in real engineering…
A recently proposed class of models attempts to learn latent dynamics from high-dimensional observations, like images, using priors informed by Hamiltonian mechanics. While these models have important potential applications in areas like…
Medical image segmentation is a fundamental and critical step in many clinical approaches. Semi-supervised learning has been widely applied to medical image segmentation tasks since it alleviates the heavy burden of acquiring…
Map-to-map matching is a critical task for aligning spatial data across heterogeneous sources, yet it remains challenging due to the lack of ground truth correspondences, sparse node features, and scalability demands. In this paper, we…
We propose UnMixMatch, a semi-supervised learning framework which can learn effective representations from unconstrained unlabelled data in order to scale up performance. Most existing semi-supervised methods rely on the assumption that…
By definition, transverse intersections are stable under infinitesimal perturbations. Using persistent homology, we extend this notion to a measure. Given a space of perturbations, we assign to each homology class of the intersection its…